CS PhD student @DrexelCCI working on formalization in Lean. Maintainer of https://xitter.cf/t.co/waYLdE0QGI. Student Researcher @GoogleDeepMind
Philadelphia, PA
Joined December 2014
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I figured my math followers would especially appreciate this! Just got these, they are originals from 1740 and 1751. Include the original publication of Euler's solution to the Basel problem, among other very cool things. So crazy to have these pieces of history on my bookshelf.
> We also expect the verification of lean4lean... Arthur Adjedj is working on the kernel renovation plan
Beneath the fold is what I consider the most important ongoing work for Lean soundness. Happy to see these projects mentioned in Leo's blog.
Lean v4.35.0 is out, and it ships with verified kernels.
Run `lake check --paranoid` to recheck your project with every bundled kernel.
Blog post: leodemoura.github.io/blog/20…
I agree, but it's also extremely difficult. Formalization makes many decisions about representation of mathematics that are equivalent, but very non-trivially so. (And then consider tactics!). A principled implementation would be a significant research/engineering effort.
Not sure I can imagine a worse target for a "you don't understand anything about math" tweet.
Chris Henson retweeted
No: a more accurate way of putting whay the say is that there are many misalignments between the natural language (NL) slop and the Lean slop, meaning the the Lean slop is a formal code for a different NL proof (different path). So long as …
A new paper shows that when AI translates a math proof into Lean, passing the Lean check says nothing about whether the original proof is right.
They show a chatbot turning a wrong proof into a valid Lean proof by silently fixing the error.
Knowing when a statement can be translated faithfully is provably harder than the Halting problem, so no AI translator can always do it.
> AI labs that release substantial mathematical output without immediate accompanying human understanding must take responsibility for ensuring that human understanding will follow
Curious to see how OAI interprets/follows through on this, I wish the blog at least hinted at it
On OpenAI’s release of mathematical results. ~ Advisory Group on Mathematics and Artificial Intelligence. proofsandprompts.com/2026/10…
#AI4Math
My wildest AI experience to date: in the middle of a Lean formalization Astra, complete unprompted, finds a Pascal program from the 90s, ports it to C++, then uses this as part of a template for much more efficient versions of numerically heavy proofs.
Very interesting work/discussion about odd properties of models of Lean and possible extensions that are nice in the sense of what independent statements remain.
#MathDay 4. SolidLean. This is my new project I alluded to yesterday. It's a system of axioms that (mostly) extends the 3 standard axioms of Lean, which provide its type theory a valuable metamathetical feature known as solidity.
Chris Henson retweeted
Super misleading to post about this without being upfront about all of the caveats and limitations, in a way that is wildly worrying because it will mislead potential funders into thinking this is a solved problem when it is very much not
Lean has a new checker: con-leche, a CONsistent LEan CHEcker. This is an external checker for Lean that is proven (in Lean) to be consistent, meaning it does not accept a proof of False.
Joachim Breitner (@nomeata) is the mastermind behind the project. github.com/leanprover/con-le…
Chris Henson retweeted
Prismriver, a Lean 4 music formalization library - talk at Lean NYC this sun (see lean.nyc), at FARM workshop at ICFP, and a free performance 8/24 evening at IU Indianapolis. we will be playing lean compositions!
arxiv.org/abs/2606.19936
Chris Henson retweeted
i bet even if claude proved 100% of the zeroes of the zeta function were on the critical line, mathematicians wouldnt call it a full proof of the riemann hypothesis
come on that's not "almost" it's 100%!!!!
ai-hating mathematicians constantly moving the goalposts smh
As much as I love categorical semantics, I get this feeling a lot. At some point it feels like an arbitrary distinction from the syntax. To me order theory, magmas, relations, etc. are impressive for the ratio of intuitive, limited axioms to the resulting math.
I'm at my quota for spicy titles given yesterday's Collatz shenanigans, but this is a very nicely written and level-headed summary of what is missing in Lean compared to Rocq. (Though I hope with increased focus on program verification this changes over the next couple of years!)
🌶️ "Why Rocq is better than Lean for program verification": A write-up on why I don't give in to the hype and switch to Lean for formal verification of programs. joomy.korkutblech.com/posts/…
I think you should thoroughly check your code before unleashing it on the world
The judgement that the *statement* of a formalization represents the informal math is inherently informal. Using AI here can perhaps be a heuristic, but it is inherently a point of trust that has to be human verified.
A proof that's formalized doesn't need to be peer-reviewed. The definitions and statement need to be verified, and you have to confirm that there aren't any cheats/axioms, but that's much, much easier, and could be done by AI to a high degree of confidence, far above the standards of any published journal.
I've been helping out a bit with this for the last couple of months. It's very fun to carefully think through the differences in presentation required for this port, especially with the folks at Penn who have so much experience teaching Rocq.
Software Foundations will be translated to Lean! 😎 Available around fall.
softwarefoundations.cis.upen…
Here’s the Zulip announcement by Benjamin C. Pierce:
leanprover.zulipchat.com/#na…
#LeanLang #LeanProver #SoftwareFoundations
An interesting read. (As I've come to always expect from Shriram!)
I've spent months rethinking and rebuilding my programming languages course from scratch for the agentic coding era. I wrote myself a memo explaining what I'm doing. I figure others might be interested in the redesign, so here goes! Feedback welcome ofc.
docs.google.com/document/d/e…
The other half missed in these conversations is that formalization is also a human endeavor! Probably the most important factor that has centered Lean for AI usage is the social convergence of a unified Mathlib, which is only possible with a huge amount of human interaction
I signed this as well. Minus some minor quibbles about how formalization is framed, I agree with the points it makes.
I have signed the Leiden declaration, and encourage everyone to read it and reflect.
Even if some of the points are impossible to achieve in reality, they are a good set of guidelines to try and do what is best for humanity.
leidendeclaration.ai/
